An explicit saturating set consisting of eigenfunctions of Stokes operator in general 3D Cylinders is proposed. The existence of saturating sets implies the approximate controllability for Navier–Stokes equations in $ \rm 3D $ Cylinders under Lions boundary conditions.

中文翻译：

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Navier–Stokes方程的近似可控性 \ begin {document} $ \ rm3D $ \ end {document} Lions边界条件下的圆柱体通过显式饱和集

提出了由Stokes算子本征函数在一般3D圆柱体中组成的显式饱和集。饱和集的存在意味着在Lions边界条件下$ \ rm 3D $圆柱中Navier–Stokes方程的近似可控性。